Collective Ion Dynamics from Finite-Volume Fluctuations in Model Explicit-Solvent Electrolytes

Abstract

Understanding how collective ion transport emerges from equilibrium fluctuations is central to electrolyte statistical mechanics. Finite-volume fluctuations provide an accessible route to this information, but their interpretation is complicated because they mix wave numbers and collective fields. Here, we extend the finite-volume counting framework for inferring collective ion diffusion by combining the exact window projection with an inertial independent-particle reference, and apply it to a symmetric 1:1 solvent primitive model. The growth of ion-number fluctuations between the ballistic and plateau regimes appears nearly ideal, but this apparent ideality results from compensation between negative structural and positive dynamical excess contributions. The coupled ion-number--solvent relaxation further reveals a signed redistribution between solvent-associated and solvent-orthogonal projections that is largely hidden in the total response. The inferred collective diffusion depends on observation length and dynamical closure: measured structure alone does not systematically improve the estimate, whereas the coupled-field description reduces the high-concentration discrepancy. These results provide a basis for analyzing more realistic electrolytes with mutually coupled ion-number, charge, and solvent fluctuations.